JEE Math Practice Question

Let [t] denote the greatest integer $$ \le $$ t. If for some $$\lambda $$ $$ \in $$ R - {1, 0}, $$\mathop {\lim }\limits_{x \to 0} \left| {{{1 - x + \left| x \right|} \over {\lambda - x + \left[ x \right]}}} \right|$$ = L, then L is equal to :

1. A.1
2. B.2
3. C.0
4. D.$${1 \over 2}$$